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A Cartan–Hadamard type result for relatively hyperbolic groups

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Abstract

In this article, we prove that if a finitely presented group has an asymptotic cone which is tree-graded with respect to a precise set of pieces then it is relatively hyperbolic. This answers a question of Mark Sapir and generalizes a result of Kapovich and Kleiner to relatively hyperbolic groups.

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Acknowledgments

The authors would like to thank Mark Sapir for introducing the question to them as well as his helpful conversations on this topic.

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Authors and Affiliations

  1. CNRS/IRMAR, Université de Rennes 1, Campus de Beaulieu, Bâtiment 22 et 23, 263 avenue du Général Leclerc, CS 74205, 35 042, Rennes Cedex, France

    Rémi Coulon

  2. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249) 851 S. Morgan Street, Chicago, IL, 60607-7045, USA

    Michael Hull

  3. Courant Institute of Mathematics, New York University, Room 1003, 251 Mercer Street, New York, NY, 10012, USA

    Curtis Kent

Authors
  1. Rémi Coulon
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  2. Michael Hull
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  3. Curtis Kent
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Correspondence to Curtis Kent.

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Coulon, R., Hull, M. & Kent, C. A Cartan–Hadamard type result for relatively hyperbolic groups. Geom Dedicata 180, 339–371 (2016). https://doi.org/10.1007/s10711-015-0105-5

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  • DOI: https://doi.org/10.1007/s10711-015-0105-5

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